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MATHEMATICS UNDERSTANDING AND HISTORY
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Rescooped by Harpal S.sandhu from MATHEMATICS-NETWORK=NATURE=BASICS
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How Signals, Geometry, and Topology are Influencing Data Science

I've been noticing unlikely areas of mathematics pop-up in data analysis. While signal processing is a natural fit, topology, differential and algebraic geometry aren't exactly areas you associate with...

Via Ed Stenson, Pierre Levy, Harpal S.sandhu
Harpal S.sandhu's insight:

DATA SCIENCE

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Generating 3D Topologies with Multiple Constraints on the GPU | hgpu.org

Generating 3D Topologies with Multiple Constraints on the GPU | Computer science, CUDA, nVidia, nVidia GeForce GTX 480, Topology optimization problem


Via Mikael Bourges-Sevenier
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gpu

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Topology of Time by Jay Weidner

In his essay, "2012 The Typology of Time Hyperdimensional Space and the Unfolding of the Four Ages,"Weidner describes an imminent end of an age. The alchemical researcher provides details as we approach the 'null point' of time. The Yuga system of Hindu cosmology is represented on the Hendaye Cross, discovered Weidner. The four ages (pictured left) are Satya Yuga, Tetra Yuga, Dvapara and Kali Yuga and correspond to Golden, Silver, Bronze and Iron Ages. "According to the cross at Hendaye the Iron Age, or the Kali Yuga, will be coming to an end with the galactic alignment on the winter solstice of December 21st 2012," writes Weidner.


Via 11th Dimension Team
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time

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Spatial Topology | GISDoctor.com

The concept of topology isn’t something that every spatially enabled person fully understands. That is OK, because I too had to learn (and relearn) how spatial topology works over the years, especially early on back in the ArcView 3.X days. I think this experience is fairly typical of someone who uses GIS. If one is taking a GIS course or a course that uses GIS it is not very often that the concept of spatial topology is covered in-depth or at all. Spatial topology also may not be something that people are overly concerned about during their day-to-day workflow, meaning they may let their geospatial topology skills slide from time to time. As a public service here is a basic overview of geospatial topology.

 

First question: What is topology?

You have probably heard the term topology before, whether it was in a GIS course where the instruction lightly glazed over the topic, or in a geometry /mathematics course.

 

Technically speaking, topology is a field of mathematics/geometry/graph theory, that studies how the properties of a shape remain under a number of different transformations, like bending, stretching, or twisting. The field of topology is well established within mathematics and far more complicated than I wish to get in this post.


Via Elpidio I F Filho
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Dynamics and Structure in Cell Signaling Networks: Off-State Stability and Dynamically Positive Cycles

Dynamics and Structure in Cell Signaling Networks: Off-State Stability and Dynamically Positive Cycles | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

The signaling system is a fundamental part of the cell, as it regulates essential functions including growth, differentiation, protein synthesis, and apoptosis. A malfunction in this subsystem can disrupt the cell significantly, and is believed to be involved in certain diseases, with cancer being a very important example. While the information available about intracellular signaling networks is constantly growing, and the network topology is actively being analyzed, the modeling of the dynamics of such a system faces difficulties due to the vast number of parameters, which can prove hard to estimate correctly. As the functioning of the signaling system depends on the parameters in a complex way, being able to make general statements based solely on the network topology could be especially appealing. We study a general kinetic model of the signaling system, giving results for the asymptotic behavior of the system in the case of a network with only activatory interactions. We also investigate the possible generalization of our results for the case of a more general model including inhibitory interactions too. We find that feedback cycles made up entirely of activatory interactions (which we call dynamically positive) are especially important, as their properties determine whether the system has a stable signal-off state, which is desirable in many situations to avoid autoactivation due to a noisy environment. To test our results, we investigate the network topology in the Signalink database, and find that the human signaling network indeed has only significantly few dynamically positive cycles, which agrees well with our theoretical arguments.


Via Ashish Umre
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network

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InfoSec Institute Resources – Network Topology

InfoSec Institute Resources – Network Topology | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
IDS: An intrusion detection system can be software-based or hardware-based and is used to monitor network packets or systems for malicious activity and do a specific action if such activity is detected.

Via Daniel A. Libby, CFC
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network

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How to Design a Network Topology in PowerPoint Using Shapes | PowerPoint Presentation

How to Design a Network Topology in PowerPoint Using Shapes | PowerPoint Presentation | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

Using Shapes in PowerPoint you can create awesome diagrams and graphics for your presentations. In this case we will show you how to design a simple physical network topology diagram in PowerPoint. This can be really helpful for a network course in computer engineering courses as well as other networking and connectivity presentations.


Via FPPT
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power

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How Did Topological Data Analysis (TDA) Lead to the Birth of Ayasdi?

How Did Topological Data Analysis (TDA) Lead to the Birth of Ayasdi? | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

http://www.ayasdi.com/

 

Topological Data Analysis (TDA) brings together mathematics with computer science, and uses algorithms and concepts from algebraic topology to extract insights from complex multi-dimensional data structures. In more layman’s terms: Topological Data Analysis studies the underlying shape of data with the principle that “Data has Shape, Shape has Meaning.”

 

While Topological Data Analysis (TDA) may seem like something only for math people, Ayasdi’s founder and Stanford Mathematics Professor Gunnar Carlsson had a goal to make TDA into something that anyone could use without having a Ph.D. in mathematics.


Via Ashish Umre
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data analysis

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Robustness of cooperation on scale-free networks under continuous topological change

In this paper, we numerically investigate the robustness of cooperation clusters in prisoner's dilemma played on scale-free networks, where their network topologies change by continuous removal and addition of nodes. Each of these removal and addition can be either random or intentional. We therefore have four different strategies in changing network topology: random removal and random addition (RR), random removal and preferential addition (RP), targeted removal and random addition (TR), and targeted removal and preferential addition (TP). We find that cooperation clusters are the most fragile against TR, while they are the most robust against RP even in high temptation coefficients for defect. The effect of the degree mixing pattern of the network is not the primary factor for the robustness of cooperation under continuous change in network topology due to consequential removal and addition of nodes, which is quite different from the cases observed in static networks. Cooperation clusters become more robust as the number of links of the hubs occupied by cooperators increase. Our results indicate that a huge variety of individuals are needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.

 

Robustness of cooperation on scale-free networks under continuous topological change

Genki Ichinose, Yuto Tenguishi, Toshihiro Tanizawa

http://arxiv.org/abs/1306.3007


Via Complexity Digest
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robustness

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Online Math Programs | Math Practice & Learning

Online Math Programs | Math Practice & Learning | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Online Math Programs with Interactive math worksheets, hints, video Lessons.

Via Ann Marie Davis Bishop
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WORKSHEETS

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Top 40 + math concepts = Musical mathematics | UWM News

Top 40 + math concepts = Musical mathematics | UWM News | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Zach Steffes has been creating math-related musical parodies that supplement his classroom instruction and lectures.

Via Ann Marie Davis Bishop
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CONCEPTS

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Millions of Free eBooks and Audio Books Online

Millions of Free eBooks and Audio Books Online | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
  Introduction: This is the launch page for the pages here at Gizmo's Tech Support Alert that list sites with free ebooks and audiobooks. There are 3 pages that separate sites on the format of the ebooks, Kindle, ePub and Online reading

 

.This site divides millions of free ebooks and audio books into subjects and genres (biographies, children, teen and young adult, comic ebooks, culinary, health and fitness, humor and comedy, mystery and thrillers, travel, romance, science fiction,  textbooks, history, religion, math, philosophy, etc.). If you don't have time to look through the site now, why not bookmark it.

 

More here: http://www.techsupportalert.com/free-ebooks-audio-books


Via Fe Angela M. Verzosa
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LIBRARY

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Finally: Gödel's Proof of Incompleteness! | Good Math, Bad Math

Finally: Gödel's Proof of Incompleteness! | Good Math, Bad Math | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Encoding meta-math arithmetically: how to take meta-mathematical properties of logical statements, and define them as arithmetic properties of the Gödel numberings of the statements. This was step 2 proper.
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GODEL

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How Signals, Geometry, and Topology are Influencing Data Science

I've been noticing unlikely areas of mathematics pop-up in data analysis. While signal processing is a natural fit, topology, differential and algebraic geometry aren't exactly areas you associate with...

Via Ed Stenson, Pierre Levy, Harpal S.sandhu
Harpal S.sandhu's insight:

data science

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Profile of math-inspired 3D printing sculptor Bathsheba Grossman - Boing Boing

Profile of math-inspired 3D printing sculptor Bathsheba Grossman - Boing Boing | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Boing Boing Profile of math-inspired 3D printing sculptor Bathsheba Grossman Boing Boing I was originally a math major interested in geometry and topology, when as a college senior I met the remarkable sculptor Erwin Hauer, and suddenly it was...

Via VERONICA LESTER
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3d

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Functional modules, structural topology, and optimal activity in metabolic networks

Functional modules, structural topology, and optimal activity in metabolic networks | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

Modular organization in biological networks has been suggested as a natural mechanism by which a cell coordinates its metabolic strategies for evolving and responding to environmental perturbations. To understand how this occurs, there is a need for developing computational schemes that contribute to integration of genomic-scale information and assist investigators in formulating biological hypotheses in a quantitative and systematic fashion. In this work, we combined metabolome data and constraint-based modeling to elucidate the relationships among structural modules, functional organization, and the optimal metabolic phenotype of Rhizobium etli, a bacterium that fixes nitrogen in symbiosis with Phaseolus vulgaris. To experimentally characterize the metabolic phenotype of this microorganism, we obtained the metabolic profile of 220 metabolites at two physiological stages: under free-living conditions, and during nitrogen fixation with P. vulgaris. By integrating these data into a constraint-based model, we built a refined computational platform with the capability to survey the metabolic activity underlying nitrogen fixation in R. etli. Topological analysis of the metabolic reconstruction led us to identify modular structures with functional activities. Consistent with modular activity in metabolism, we found that most of the metabolites experimentally detected in each module simultaneously increased their relative abundances during nitrogen fixation. In this work, we explore the relationships among topology, biological function, and optimal activity in the metabolism of R. etli through an integrative analysis based on modeling and metabolome data. Our findings suggest that the metabolic activity during nitrogen fixation is supported by interacting structural modules that correlate with three functional classifications: nucleic acids, peptides, and lipids. More fundamentally, we supply evidence that such modular organization during functional nitrogen fixation is a robust property under different environmental conditions.

 

Resendis-Antonio O, Hernández M, Mora Y, Encarnación S. (2012).  PLoS Comput Biol. 2012 Oct;8(10):e1002720.


Via IvanOresnik
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modules

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Dark Roasted Blend: Topological Marvel: The Klein Bottle in Art

Dark Roasted Blend: Topological Marvel: The Klein Bottle in Art | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

A geometric enigma, a convoluted mind-bender dropped upon us from the wonderful extra-dimensional realm of topology, the Klein Bottle is perhaps even popular with artists and architects than the ubiquitous Moebius strip. In fact, the Klein Bottle is what happens when you merge two Moebius Strips together: the resulting shape will still have only one side - with its inside and outside merging into one!


Via Jukka Melaranta
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klien

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Mathematical Art Presented by the American Mathematical Society

Mathematical Art Presented by the American Mathematical Society | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

"The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

 

"Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more."

 


Via Jim Lerman, Alessandro Rea
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BookChook's curator insight, May 31, 2013 6:52 PM

Help kids connect Maths with Art 

Cameron Brotherton -Jennings's comment, May 31, 2013 10:40 PM
Music Mathematics Man
MsPedagogicalProwess's curator insight, April 13, 2014 12:28 AM

Provides an insight into the cross integration between Maths and Arts. This is a great link, for a foray into higher order thinking, and visualisation. Could be a valuable resource for upper primary, in linking their mathematical learning to a more meaning context (in linking to their experiences of art in nature and in man-made objects around them) –


There are links to galleries & exhibitions – which could translate into a class excursion. 

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Tying Knots with Light: Spontaneous knotting of self-trapped light waves

Tying Knots with Light: Spontaneous knotting of self-trapped light waves | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

A new theory and simulations have been developed that describe a spinning optical soliton whose propagation spontaneously excites knotted and linked optical vortices. The nonlinear phase of the self-trapped light beam breaks the wave front into a sequence of optical vortex loops around the soliton, which, through the soliton's orbital angular momentum and spatial twist, tangle on propagation to form links and knots. Similar spontaneous knot topology should be a universal feature of waves whose phase front is twisted and nonlinearly modulated, including superfluids and trapped matter waves.


Via Dr. Stefan Gruenwald
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knots

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How Signals, Geometry, and Topology are Influencing Data Science

I've been noticing unlikely areas of mathematics pop-up in data analysis. While signal processing is a natural fit, topology, differential and algebraic geometry aren't exactly areas you associate with...

Via Ed Stenson, Pierre Levy
Harpal S.sandhu's insight:

geometry

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Harpal S.sandhu's curator insight, July 9, 2013 6:20 PM

data science

Harpal S.sandhu's curator insight, July 15, 2013 5:25 PM

DATA SCIENCE

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Temporal dynamics and network analysis

Temporal dynamics and network analysis | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

Summary

1. Network analysis is widely used in diverse fields and can be a powerful framework for studying the structure of biological systems. Temporal dynamics are a key issue for many ecological and evolutionary questions. These dynamics include both changes in network topology and flow on the network. Network analyses that ignore or do not adequately account for the temporal dynamics can result in inappropriate inferences.

2. We suggest that existing methods are currently under-utilized in many ecological and evolutionary network analyses and that the broader incorporation of these methods will considerably advance the current field. Our goal is to introduce ecologists and evolutionary biologists interested in studying network dynamics to extant ideas and methodological approaches, at a level appropriate for those new to the field.

3. We present an overview of time-ordered networks, which provide a framework for analysing network dynamics that addresses multiple inferential issues and permits novel types of temporally informed network analyses. We review available methods and software, discuss the utility and considerations of different approaches, provide a worked example analysis and highlight new research opportunities in ecology and evolutionary biology.


Via Ashish Umre
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dynamics in systems

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Math Review: Computation, Algebra, Geometry (Core Skills Series ...

Math Review: Computation, Algebra, Geometry (Core Skills Series ... | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Math Review: Computation, Algebra, Geometry (Core Skills Series, Middle School Math) book download STECK-VAUGHN Download Math Review: Computation, Algebra, Geometry (Core Skills Series, Middle School Math) ThinkCentral Welcome to ThinkCentral.
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Classroom Freebies Too: Math Wheels

Classroom Freebies Too: Math Wheels | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Math games and centers are one of my favorite things to make. I have found teachers need additional resources in this area because traditional math programs don't usually include them, or if they do, they don't cover many ...

Via Ann Marie Davis Bishop
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WHEELS

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The Great Courses

The Great Courses | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
University-level courses for lifelong learning from the world's top professors. Educational facts and video clips on science, math, art, music, philosophy, b...

Via Troy Mccomas (troy48)
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GREAT SOURCE

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Multiplication of a vector by a scalar: Geometric approach | Math ...

Math Support at Visions Visions In Education. Home ... Multiplication of a vector by a scalar: Geometric approach ... Solving a linear equation with several occurrences of the variable: Fractional forms with binomial numerators ...
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VECTORS

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